In various embodiments, a workpiece is processed utilizing one or more output beams emitted from a step-core optical fiber and formed from one or more input beams that may have non-circular beam shapes. In various embodiments, an input beam may be a variable-power laser beam having a laser-beam numerical aperture (NA) that varies as a function of the power of the laser beam. The step-core optical fiber may have an outer core NA that is greater than or equal to the laser-beam NA at a laser power of approximately 100%, an inner core NA that is less than or equal to the outer core NA, and an inner core NA that is greater than or equal to the laser-beam NA at a power of 50%.